How to make a grainy material in Blender Cycles?
Use a noise texture. You can change the scale and detail. Hooking it up to a Color Ramp (or curve, or gamma or Bright/Contrast) node will allow you to set the contrast  

You can set the color directly.



Or use the texture to control the mix of other colors.



Or different shaders.



Or you can use it to combine with other textures and types of noise, as described in this answer: How do I make a Decal look worn?